The Effect of Random Threshold Levels on PCM Quantization Noise

Abstract

It is common with PCM systems to consider a uniform quantization noise (or error) distribution over plus or minus one half the quantization level. This distribution must be modified to describe the effect of uncertainties in the location of the decision thresholds which separate adjacent quantization levels. The uncertainties exist because electronic decision circuits trigger somewhere within a narrow band surrounding an intended voltage instead of at exactly that voltage. In this paper the encoding error distributions, are calculated in terms of the distributions of the threshold locations. It is shown that the variance of the quantization noise is increased by an amount almost exactly equal to the variance of the threshold uncertainty distribution. The effect of the uncertainty bands becomes noticeable only where the uncertainty band is an appreciable part of the quantization interval. Prime examples are systems with small voltage differences between encoding levels such as low-level systems (0 to 50 millivolts) and systems with large number of quantization levels. Because error variance is related to the square of the uncertainty range, a threshold uncertainty range of 1/10 the quantization interval will increase the net encoding variance by approximately (1/10)² or 1.0%.